%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/conic_equal_area-1.0.0"
title: |
  Alber's conic equal area projection.

description: |
  Corresponds to the `COE` projection in the FITS WCS standard.

  See
  [conic](ref:schemas/conic-1.0.0)
  for the definition of the full transformation.

  The transformation is defined as:

  $$C &= \gamma / 2 \\
    R_\theta &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin \theta} \\
    Y_0 &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin((\theta_1 + \theta_2)/2)}$$

  where:

  $$\gamma = \sin \theta_1 + \sin \theta_2$$

  Invertibility: All ASDF tools are required to provide the inverse of
  this transform.

allOf:
  - $ref: "conic-1.0.0"
...
